An apparatus of the type described above is normally required when a stream of adjacent and consecutive layers or stacks of sheets transported by belts or pushers are deposited on a table and are to be transferred in to a row of successive layers of sheets running transversely to it. In this arrangement, faster running belts are connected to the transverse transporter which place the individual layers a certain distance apart, that is to say separate the individual layers. It has been proposed that this transverse transportation takes place on the faster running belts by means of pushers which act on the layers transversely to their original transporting direction and pushes them over in unison. However, it may happen that the layers slide into each other, like playing cards during shuffling, and thus lead to disturbances. It is thus essential for the individual layers of sheets to follow each other, that is to say usually to be brought into contact with each other or brought to a certain constant distance from one another, so that a constant distance is ensured during the subsequent separation.